Hello kakkemajjj, welcome to Sysnative!
Yes, the 0x800F0900 and 0x800B0100 errors are the most common errors we run into, but fortunately it's a nice easy fix!
Windows Update Package Replacement
Warning: this fix is specific to the user in this thread. No one else should follow these instructions as it may cause more harm than good. If you are after assistance, please start a thread of your own.
- Please download the attached file, WUA_64.zip and save this to your Desktop.
- Right-click on the file and select Extract All...
- Tick the box labelled Show extracted files when complete then click Extract
- A window will open showing two folders, Manifests and Packages
- Open the Manifests folder and copy the files into the following folder (if there are any files)
C:\Windows\Temp\CheckSur\Winsxs\Manifests
- Open the Packages folder and copy the files into the following folder (if there are any files)
C:\Windows\Temp\CheckSur\Servicing\Packages
- Run the System Update Readiness Tool (SURT) again
- When the SURT finishes installing, copy (Ctrl + C) and paste (Ctrl + V) the contents of the SURT log into your next post please:
C:\Windows\Logs\CBS\CheckSUR.persist.log
https://dl.dropboxusercontent.com/u/16537616/Fixes/SURT/~Generic/WUA_64.zip
Tom